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11.3 Exercise 38

Avg difficulty 2.5

fXY(t,u)=2411tuf_{X Y} \left(t , u\right) = \frac{24}{11} t u for 0≤t≤20 \leq t \leq 2, 0≤u≤min{1,2-t}0 \leq u \leq \min \left\{1 , 2 - t\right\} (see the exercise).

Z = I M ( X , Y ) 1 2 X + I M c ( X , Y ) Y 2 , M = { ( t , u ) : u > t } Z = I_{M} \left(X , Y\right) \frac{1}{2} X + I_{M^{c}} \left(X , Y\right) Y^{2} , M = \left\{\left(t , u\right) : u > t\right\}

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 38

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.